To fully characterize the microstructure of a two-phase medium as well as its effective physical properties, an infinite set of \(n\) -point correlation functions are required in the infinite-volume limit [1]}. A variety of different types of such correlation functions arise in rigorous theories that depend on the bulk physical property of interest [1]}. For example, there is the standard \(n\) -point correlation function \(S^{(i)}_n(\mathbf {x}_1,...,\mathbf {x}_n)\)  which gives the probability that the position vectors \(\mathbf {x}_1,...\mathbf {x}_n\)  all lie in phase \(i\)  where \(i=1,2\)  for two-phase media (see Sec.  for details) [1]}, [4]}. Given that it is generally impossible to obtain the information contained in such an infinite set of correlation functions, their lower-order versions are often used as a starting point to characterize the structure and physical properties of a two-phase medium.
